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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
52/2006

Convexity of the free boundary for an exterior free boundary problem involving the perimeter

Hayk Mikayelyan and Henrik Shahgholian

Abstract

We prove that if the given compact set $K$ is convex then a minimizer of the functional $$ I(v)=\int_{B_R} |\nabla v|^p dx+\text{Per}(\{v>0\}),\,1

Received:
May 18, 2006
Published:
May 18, 2006
Keywords:
free boundary problems, perimeter, convexity

Related publications

inJournal
2013 Repository Open Access
Hayk Mikayelyan and Henrik Shahgholian

Convexity of the free boundary for an exterior free boundary problem involving the perimeter

In: Communications on pure and applied analysis, 12 (2013) 3, pp. 1431-1443